DiscreteLaplace (version 1.1.1)

estdlaplace2: Sample estimation for the ADSL

Description

The function provides the point estimates for the parameters of the ASDL, resorting to four possible methods: method of moments, maximum likelihood method, method of proportion, modified method of moments. For details, please take a look at the references.

Usage

estdlaplace2(x, method = "M", err = 0.001, parml = c(exp(-1), exp(-1)))

Arguments

x

a vector of observations from the ADSL

method

M for the method of moments, ML for the maximum likelihood methods, P for the method of proportion, MM for the modified method of moments

err

a positive tolerance value, as small as possible, used in the definition of lower and upper bounds of the parameters $p$ and $q$ in the minimization algorithm utilized by the method of moments

parml

starting values for $p$ and $q$ in the optimization process for the maximum likelihood method

Value

a vector with the parameter estimates of $p$ and $q$.

References

A. Barbiero, An alternative discrete Laplace distribution, Statistical Methodology, 16: 47-67

See Also

dlaplacelike2

Examples

p <- 0.4
q <- 0.6
x <- rdlaplace2(n=100, p, q)
est <- matrix(0, 5, 2)
est[1,] <- c(p,q)
est[2,] <- estdlaplace2(x, method="M")
est[3,] <- estdlaplace2(x, method="ML")
est[4,] <- estdlaplace2(x, method="P")
est[5,] <- estdlaplace2(x, method="MM")
dimnames(est)[[1]]<-c("true","M","ML","P","MM")
dimnames(est)[[2]]<-c("p","q")
xlim <- c(min(est[,1])*.98,max(est[,1])*1.02)
ylim <- c(min(est[,2])*.98,max(est[,2])*1.02)
plot(est, pch=19, col=1:5, xlim=xlim, ylim=ylim)
text(est, dimnames(est)[[1]], pos=3, col=1:5, cex= .75)